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8th Class Mathematics Exponents and Power Question Bank Exponents and Powers

  • question_answer
    If \[{{2}^{2x-y}}=32\] and \[{{2}^{x+y}}=16\] then find \[{{\mathbf{x}}^{\mathbf{2}}}+{{\mathbf{y}}^{\mathbf{2}}}\]is equal to

    A)  9                                

    B)  10  

    C)  11                               

    D)  13

    Correct Answer: B

    Solution :

    (b) \[{{2}^{2x-y}}=32\] \[\Rightarrow 2x-y=5\]                             ??..(1) \[\Rightarrow {{2}^{x+y}}=16\Rightarrow x+y=4\]          ??(2) Adding (1) & (2) \[\Rightarrow 3x=9\Rightarrow x=3\] \[\Rightarrow y=4-3=1\] \[\therefore {{x}^{2}}+{{y}^{2}}={{3}^{2}}+{{1}^{2}}=10\].


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